Given a surface M in Euclidean space, we have the generalized-Gauss-map G, i.e. map the tangent spaces into the Grassmannian G(2,n). What is the relation between DG and the second fundamental form of M, and the Gauss curvature?

Sorry about deleting my answer so quickly but I pushed the preview button while the page was jumping around due to rendering and I missed! Full answer available soon I hope!
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drbobmeisterFeb 23 '11 at 7:33

Damn! Did it again. Very sorry! Answer almost ready.
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drbobmeisterJun 9 '11 at 23:36